Central value of automorphic L-functions

Ehud Moshe Baruch, Zhengyu Mao

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


We prove a generalization to the totally real field case of the Waldspurger's formula relating the Fourier coefficient of a half integral weight form and the central value of the L-function of an integral weight form. Our proof is based on a new interpretation of Waldspurger's formula as a combination of two ingredients - an equality between global distributions, and a dichotomy result for theta correspondence. As applications we generalize the Kohnen-Zagier formula for holomorphic forms and prove the equivalence of the Ramanujan conjecture for half integral weight forms and a case of the Lindelöf hypothesis for integral weight forms. We also study the Kohnen space in the adelic setting.

Original languageEnglish (US)
Pages (from-to)333-384
Number of pages52
JournalGeometric and Functional Analysis
Issue number2
StatePublished - Jun 2007

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology


  • Half integral weight forms
  • Special values of L-functions
  • Waldspurger correspondence


Dive into the research topics of 'Central value of automorphic L-functions'. Together they form a unique fingerprint.

Cite this